Question

Q.5 The number of vertices in a polyhedron which has 12 faces and 30 edges is

(a) 40 (b) 16 (c) 18 (d) 20​

Answer 1

Answer:

20

Step-by-step explanation:

Euler's polyhedron formula, V−E+F=2

Euler's polyhedron formula, V−E+F=2V = number of vertices

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edges

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of faces

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of facesSo, 12−30+F=2

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of facesSo, 12−30+F=2F−18=2

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of facesSo, 12−30+F=2F−18=2F=18+2

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of facesSo, 12−30+F=2F−18=2F=18+2F=20

Euler's polyhedron formula, V−E+F=2V = number of verticesE = number of edgesF = number of facesSo, 12−30+F=2F−18=2F=18+2F=20Number of faces = 20.